This invention relates to two-dimensional inverse discrete cosine transforming.
Image compression techniques such as JPEG (joint photographic experts group) and MPEG (moving pictures experts group) use inverse discrete cosine transforms (IDCT) in decompressing images. The one-dimensional (1D) IDCT function is:
            x      ⁡              (        n        )              =                  ∑                  k          =          0                          N          -          1                    ⁢                          ⁢                        c          ⁡                      (            k            )                          ⁢                  y          ⁡                      (            k            )                          ⁢                  cos          ⁡                      [                                          π                ⁡                                  (                                                            2                      ⁢                      k                                        +                    1                                    )                                                            2                ⁢                N                                      ]                                ,          ⁢      1    ≤    k    ≤          N      -      1        ,            c      ⁡              (        k        )              =          {                                                  1                              N                                                                        k              =              0                                                                                          2                N                                                                        1              ≤              k              ≤              N                                          Decompressing can also be done in two dimensions using two-dimensional (2D) IDCTs. The 2D IDCT is:
            x      ⁡              (                  i          ,          j                )              =                  ∑                  s          =          0                          S          -          1                    ⁢                          ⁢                        ∑                      t            =            0                                T            -            1                          ⁢                                  ⁢                              c            ⁡                          (                              s                ,                t                            )                                ⁢                      d            ⁡                          (                              s                ,                t                            )                                ⁢                      y            ⁡                          (                              s                ,                t                            )                                ⁢                      cos            ⁡                          [                                                                    π                    ⁡                                          (                                                                        2                          ⁢                          s                                                +                        1                                            )                                                        ⁢                  i                                                  2                  ⁢                  S                                            ]                                ⁢                      cos            ⁡                          [                                                                    π                    ⁡                                          (                                                                        2                          ⁢                          t                                                +                        1                                            )                                                        ⁢                  j                                                  2                  ⁢                  T                                            ]                                            ,          ⁢      1    ≤    s    ≤          S      -      1        ,      1    ≤    t    ≤          T      -      1        ,          ⁢            c      ⁡              (                  s          ,          t                )              =          {                                                                                    1                                      S                                                                                                                    i                    =                    0                                    ,                                      j                    =                    0                                                                                                                                            2                    S                                                                                                                    1                    ≤                    i                    ≤                                          S                      -                      1                                                        ,                                      1                    ≤                    j                    ≤                                          S                      -                      1                                                                                                    ⁢                                          ⁢                      d            ⁡                          (                              s                ,                t                            )                                      =                  {                                                                      1                                      T                                                                                                                    i                    =                    0                                    ,                                      j                    =                    0                                                                                                                                            2                    T                                                                                                                    1                    ≤                    i                    ≤                                          T                      -                      1                                                        ,                                      1                    ≤                    j                    ≤                                          T                      -                      1                                                                                                              
As shown in FIGS. 1 and 2, a decompression process 15 may be performed on a succession of images 70, e.g., video images, each image 70 broken into a sequence of one or more pixel blocks 72, e.g., 8×8 pixel blocks. An IDCT function 11 (implementing the 1D and/or 2D equation above) does not work directly on each pixel block 72 in each image, but on a sequence of matrices, e.g., 8×8 matrices of integer coefficients, associated with respective pixel blocks 72 and delivered from a de-quantizer block 13 (another part of the decompression process 15).